Question

An ASPCA statistic stated that 31% of cat owners obtain their felines from animal shelters/humane societies. I believe this has increased since this statistic was published. To test my claim, I asked 100 cat owners if they obtained their felines from animal shelters/humane societies, and 62 of them said yes. I will test this at the 0.05 significance level.

Answer 1

Solution :

Given that,

= 0.31

1 - = 0.69

n = 100

x = 62

Level of significance = = 0.05

Point estimate = sample proportion = = x / n = 0.62

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.31

Ha: p 0.31

Test statistics

z = ( - ) / *(1-) / n

= ( 0.62 - 0.31) / (0.31*0.69) / 100

= 6.703

P-value = P(Z>z)

= 1 - P(Z <z )

= 1- P(Z < 6.703)

= 1 - 1

= 0.000

The p-value is p = 0.0, and since p = 0. < 0.05, it is concluded that the null hypothesis is rejected.

Conclusion:

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that I believe this has increased since this statistic was published at the α = 0.05 significance level.